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A firm uses labor and machines to produce output according to the production function f(L; M) = 0

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A firm uses labor and machines to produce output according to the production function f(L; M) = 0.1 LT2M2, where L is the number of units of labor used and M is the number of machines. The cost of labor is $10 per unit and the cost of using a machine is $40. a. On the graph below, draw an isocost line for this firm, showing combinations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. What is the slope of these isocost lines? b. How many units of labor and how many machines would the firm use to produce y units in the cheapest possible way? How much would this cost? c. On the graph, sketch the production isoquant corresponding to an output of 40. Calculate the amount of labor and the number of machines that are used to produce 40 1 Intermediate Microeconomics Cost minimization & Cost curves units of output in the cheapest possible way, given the above factor prices. Calculate the cost of producing 40 units. d. Suppose that in short run the units of machine that the firm uses is fixed at M=100. What will the cost function be?